1

解答:

>> clear

>> syms x

>> limit(x^2/exp(x),x,+inf)

 ans =

 0

 

2

解答:

>> clear

>> syms x

>> limit(x^2*log(x),x,0,'right')

 ans =

 0


 

3

解答:

>> clear

>> syms x

>> limit((exp(x)-exp(-x)-2*x)/(x-sin(x)),x,0,'right')

 ans =

 2


 

 

4、讨论极限

观察的图形,判断n趋于无穷时的极限,并对具体的x值,用limit命令验证。

 

解答

解答一:

clear

x=0:0.1:4*pi;

n=1:1:100;

[x,n]=meshgrid(x,n);

z=cos(x).^n;

surf(x,n,z)

解答二:

>> clear

>> x=0:0.1:4*pi;

>> y=cos(x).^5;

>> plot(x,y)

>> clear

>> x=0:0.1:4*pi;

>> y=cos(x).^1001;

>> plot(x,y)

clear

x=0:0.1:4*pi;

y=cos(x).^100001;

plot(x,y,'+')

 

讨论:

对情况一,

>> clear

>> syms n

>> limit(cos(1)^n,n,+inf)

 ans =

 0

对情况二,

>> clear

>> syms n

>> limit(cos(0)^n,n,+inf)

 ans =

 1

对情况三,

>> clear

>> syms n

>> limit(cos(pi)^n,n,+inf)

 ans =

 -1 .. 1

对情况四,

>> clear

>> syms n

>> limit(cos(pi/2)^n,n,+inf)

 ans =

 0

所以,